publication . Article . 2017

Multiple Homoclinic Solutions for a Class of Superquadratic Fourth-order Differential Equations

Mohsen Timoumi;
Open Access English
  • Published: 01 Dec 2017 Journal: General Letters in Mathematics, volume 3, issue 3, pages 154-163 (issn: 2519-9269, eissn: 2519-9277, Copyright policy)
  • Publisher: Refaad
Abstract
Applying a Symmetric Mountain Pass Theorem, we prove the existence of infinitely many homoclinic solutions for a class of fourth-order differential equations u(4)(x) + ωu00(x) + a(x)u(x) = f(x,u(x)), ∀x ∈R where a ∈ C(R,R) may be negative on a bounded interval and F(x,u) =Ru 0 f(x,t)dt is superquadratic at infinity in the second variable but does not need to satisfy the well-known Ambrosetti-Rabinowitz superquadratic growth condition
Subjects
free text keywords: Fourth-order differential equation, homoclinic solutions, variational methods, Symmetric Mountain Pass Theorem, lcsh:Mathematics, lcsh:QA1-939
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